Question

prove that only one of the numbers n, n + 1 or n + 2 is divisible by 3 where n is any positive integer. Explain.​

Answer 1

Answer:

⇔

Since n, n+1, n+2 are three consecutive integers then there must be one number divisible by 3 at least. If the remainder at dividing n by 3 is 1, then n+2 must be divisible by 3 and if the remainder at dividing n by 3 is 2, then n+1 must be divisible by 3. Similarly for n+1 and n+2. Let n be divisible by 3

Answer 2

Answer:

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LET the number be (3q+r)

If n=3q then,numbers are 3q+,(3q+1),(3q+2)

=3q is divisible by 3

If n=3q+1 then,numbers are (3q+1),(3q+3),(3q+4)

=(3q+3) is divisible by 3

if n=3q+2 then,numbers are (3q+2),(3q+4),(3q+6)

=(3q+6) is divisible by 3

》out of n ,(n+2) and (n+4) only one is divisible by 3

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